Accessing the geometric origin of shift current in noncentrosymmetric quantum materials is essential for understanding nonlinear photoresponses governed by band geometry and Berry connections. We present a quantum-algorithmic approach, implemented on a classical simulator of quantum circuits, to compute the shift current in a phase-coherent and gauge-consistent manner. By expressing the geometric ingredients of the bulk photovoltaic effect as observables accessible within a quantum-circuit framework, the method enables the evaluation of the second-order dc photocurrent without explicit gauge fixing. Using the one-dimensional Rice–Mele model as a benchmark, we obtain shift-current spectra in quantitative agreement with classical calculations and exhibiting smooth behavior across the Brillouin zone. These results position quantum algorithms as a promising framework for addressing shift-current responses and, more broadly, nonlinear optical phenomena in quantum materials.
Accessing the geometric origin of shift current in noncentrosymmetric quantum materials is essential for understanding nonlinear photoresponses governed by band geometry and Berry connections. We present a quantum-algorithmic approach, implemented on a classical simulator of quantum circuits, to compute the shift current in a phase-coherent and gauge-consistent manner. By expressing the geometric ingredients of the bulk photovoltaic effect as observables accessible within a quantum-circuit framework, the method enables the evaluation of the second-order dc photocurrent without explicit gauge fixing. Using the one-dimensional Rice–Mele model as a benchmark, we obtain shift-current spectra in quantitative agreement with classical calculations and exhibiting smooth behavior across the Brillouin zone. These results position quantum algorithms as a promising framework for addressing shift-current responses and, more broadly, nonlinear optical phenomena in quantum materials.
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing n-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain.
Quantum geometry – including both the quantum metric and Berry curvature – arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
The photogalvanic effect (PGE), a fundamental nonlinear optical phenomenon in non-centrosymmetric materials, generates direct photocurrent under polarized light. Using quantum kinetic theory within the relaxation-time approximation, we theoretically investigate the PGE as a probe of quantum geometry in anisotropic type-I and type-II semi-Dirac (SD) systems, characterized by distinct electronic structures. We systematically analyse various microscopic contributions to the PGE conductivity, including injection, shift, resonance, higher-order pole, and anomalous terms, and emphasize their connections to different quantum geometric quantities, namely, Berry curvature, quantum metric, and metric connection. By studying the frequency and chemical-potential dependence of the PGE conductivity in SD systems, we find that the optical conductivities in the type-II case are significantly enhanced relative to those in type-I. For the circular PGE (CPGE), Berry-curvature-driven contributions remain qualitatively similar in both phases, whereas the linear PGE (LPGE) displays clear qualitative differences. In particular, the xxx component of the shift conductivity in the type-II phase reverses sign upon tuning the perturbation parameter δ, providing a direct signature of the Lifshitz transition. In contrast, other components remain sign-invariant, as in type-I SD systems. These combined CPGE and LPGE signatures provide an unambiguous distinction between the two SD phases. The predicted effects, realizable in TiO2/VO2 heterostructures, establish PGE as a sensitive probe of quantum geometry with potential applications in polarization-selective photodetection, optical rectification, and next-generation optoelectronic devices.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a nonlinear Drude-like part and an intrinsic term determined by the fully symmetrized normalized quantum metric dipole. Notably, we predict a previously unrecognized intrinsic Ohmic conductivity arising from band geometry in the bilinear magnetoelectric response, which exhibits transverse behavior similar to its optical counterpart. Using a two-dimensional Dirac model, we demonstrate that this geometrically induced nonlinear Ohmic response is observable in materials with high Fermi velocity and narrow band gaps. Our work provides a systematic quantum field-theoretic framework for describing nonlinear Ohmic transport in condensed matter systems.